With America focused on Harvey's extreme flooding, a series of responses, varying in scope, have come from the USA and its allies since North Korea's audacious launch of a ballistic missile that flew over Japan on Tuesday.
The two leaders pledged to continue to apply strong diplomatic and economic pressure on North Korea and to make all necessary preparations to defend against the growing threat by the North, the White House said.
It said this was a "curtain-raiser" for the North's "resolute countermeasures" against ongoing US-South Korean military drills.
Trump and Moon, speaking by phone on Friday, also discussed North Korean's "continued destabilizing and escalatory behavior", the White House said in a statement.
German Chancellor Angela Merkel and French President Emmanuel Macron said they planned to tighten European Union sanctions.
Missile over Japan is just the start, North Korea warns
This week's provocative missile launch by North Korea reminds the rest of the world's nations Kim Jong Un plays by his own rules. Kim previously threatened to send multiple missiles toward Guam, a USA territory, but instead launched just one over Japan.
Later on Sunday, Russian President Vladimir Putin met his Chinese counterpart Xi Jinping in China where they agreed to "appropriately deal with" the crisis, Chinese state news agency Xinhua said.
"But at the political level, there is no question of deploying American tactical missiles in South Korea, for the simple reason that that would fully justify, even in the eyes of the South Korean and American public, all the actions of this country [North Korea] in building its nuclear weapons".
"The worldwide community must treat this new provocation with the utmost firmness, in order to bring North Korea to come back unconditionally to the path of dialogue and to proceed to the complete, verifiable and irreversible dismantling of its nuclear and ballistic programme", he said in a statement.
Wednesday: Mixed messages from USA leadersUS Secretary of Defense James Mattis(L) and South Korea's Defense Minister Song Young-moo listen to their respective national anthems August 30, 2017 upon Young-moo's arrival at the Pentagon in Washington, DC.
Britain's foreign secretary Boris Johnson said: "They (North Korea) seem to be moving closer towards a hydrogen bomb which, if fitted to a successful missile, would unquestionably present a new order of threat", adding that there were no palatable military solutions.
"Today's nuclear test by the Democratic People's Republic of Korea (DPRK) is an extremely regrettable act".
China urged North Korea to stop "wrong" actions and said it would fully enforce United Nations resolutions on the country.
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